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一类非经典反应扩散方程的指数吸引子 被引量:2

The Exponential Attractors for a Non-classical Reaction-diffusion Equation
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摘要 利用一种新方法证明了一类非经典反应扩散方程当非线性项是任意阶多项式增长时的指数吸引子的存在性. The existence of exponential attractors for a non-classical reaction-diffusion equation is proved in this paper. When the nonlinearity is a polynomial growth of arbitrary order, corresponding conclusions will be drawn.
出处 《温州大学学报(自然科学版)》 2013年第3期52-55,共4页 Journal of Wenzhou University(Natural Science Edition)
基金 国家自然科学基金(11261027)
关键词 非经典反应扩散方程 指数吸引子 任意阶多项式增长 Non-classical Reaction-diffusion Exponential Attractors Polynomial Growth of Arbitrary Order
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参考文献7

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  • 2Sun C Y, Wang S Y, Zhong C K. Global attractors for a nonclassical diffusion equation [J]. Acta Math Sinica: English Series, 2007, DOI: 10.1007/s10114-005-0909-6.
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  • 4马巧珍,钟承奎.非经典反应扩散方程强解的全局吸引子(英文)[J].兰州大学学报(自然科学版),2004,40(5):7-9. 被引量:5
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二级参考文献7

  • 1Aifantis E C. On the problem of diffusion in solids[J]. Acta Mech, 1980, 37(1): 265-296.
  • 2Ting T W. Certain non-steady flows of second order fluids[J]. Arch Rational Mech Anal, 1963, 14(1):1-26.
  • 3Xiao Y L, Attractors for a nonclassical diffusion equation[J]. Acta Math Appl Sinica, English Series,2002, 18(1): 273-276.
  • 4Teman R. Infinite dimensional dynamical system in mechanics and physics(Second edition)[M]. New York: Spring-Verlag, 1997.
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  • 6Ma Q F, Wang S H, Zhong C K. Necessary and sufficient conditions for the existence of global attractor for semigroup and application[J]. Indiana University Mathematics Journal, 2002, 51(6): 1541-1559.
  • 7Claudio G, Munoz J E, Pata V. Global attractors for a semilinear hyperbolic equation in viscoelasticity[J]. J Math Anal Appl, 2001, 260(1): 83-99.

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